Three-stage Four-stage The optimal ten-stage method has SSP coefficient 6 and Shu-Osher form $$\begin{eqnarray} \beta_{i,i-1} & = & \left\{\begin{array}{cc} \frac{1}{6} & i\in\{1..4,6..9\} \\ \frac{1}{15} & i=5 \\ \frac{1}{10} & i=10 \end{array}\right. \\ \beta_{10,4} & = & \frac{3}{50} \\ \alpha_{i,i-1} & = & \left\{\begin{array}{cc} 1 & i\in\{1..4,6..9\} \\ \frac{2}{5} & i=5 \\ \frac{3}{5} & i=10 \end{array}\right. \\ \alpha_{5,0} & = & \frac{3}{5} \\ \alpha_{10,0} & = & \frac{1}{25} \\ \alpha_{10,4} & = & \frac{9}{25}. \end{eqnarray}$$ The abscissas are $$\begin{eqnarray} c = \frac{1}{6} \cdot \left( 0,1,2,3,4,2,3,4,5,6 \right)^T. \end{eqnarray}$$